Engineering Economic Analysis

Elements in Incremental Rate of Return Analysis 257

FIGURE 8-8 Benefit-cost .6%

graph for Example 8-8 data.

o $1000 $3000 $5000 $7000 $9000

Present Worth of Cost

We found a desirableA-B increment with a 10%IRRA-B.For the relationship between

AlternativesAandB,and the computed rates of return, we write:

[

Higher-cost Alt.A:

]

=

[

Alt.B:20% rate

]

+

[

Differences betweenAandB:

15% rate of return ofreturn 10% rate ofreturn ]

By selecting Alt.Awe have, in effect, acquired a 20% rate of return on $2000'and a

10% rate of return on an additional $2000, both desirable outcomes. Taken together asA,

the result is a 15% rate of return on a $4000 investment.This is economically preferable to

a 20% rate of return on a $2000 investment, assuming we seek to invest money whenever

we can identify an investment opportunity that meets our 6% MARR criterion. This implies

that we have sufficientmoney to acceptallinvestment opportunities for which the MARR

is exceeded that come to our attention. This assumption of an abundarit supply of money

is considered appropriate in most industrial analyses, but it is not likely to be valid for

individuals. The selection of an appropriate MARR is discussed in Chapter 15.

ELEMENTS IN INCREMENTAL RATE OF RETURN ANALYSIS

1. Be sure all the alternatives are identified. In textbook problems the alternatives
   will be well defined,but industrial problems may be less clear. Before proceeding, one must
   have all the mutually exclusive alternatives tabulated, including the "do-nothing" or "k~ep
   doing the same thing" alternative, if appropriate.


2. (Optional) Compute the rate of return for each alternative. If one or more
   alternatives has a rate of return equal to or greater than the minimum attractive rate of
   return (IRR 2: MARR), then any other alternativeswith an IRR less than the MARR may be
   immediately rejected. This optional step requires calculationsthat mayor may not eliminate I)
   .- -----

• -- -r

$9000

$8000

J!J$7000

I A /

'.

!.;:1

$6000

j:Q

'c; $5000

"€

$4000

-=

$3000

$2000

$1000